There is a similar proposition as Proposition REF  which gives the asymptotic complexity of the RLPN decoder used in conjunction with the [1]} or [2]} techniques for producing low weight codewords. For [1]} it is given by

propositionMMT
The asymptotic complexity exponent of the RLPN decoder based on [1]} is given by
\(\alpha _{\text{MMT}}(R) \mathop {=}\limits ^{\triangle }\min _{(\sigma ,\nu _1,\nu _2,\lambda ,\lambda _1,\omega _1,\omega _2,\pi _1) \in {{R}}} \beta (R,\sigma ,\nu _1,\nu _2,\lambda ,\lambda _1,\omega _1,\omega _2,\pi _1)\) 
